A239386 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than five standard deviations.

2, 8, 6, 6, 5, 1, 5, 7, 1, 8, 7, 9, 1, 9, 3, 9, 1, 1, 6, 7, 3, 7, 5, 2, 3, 3, 2, 8, 7, 4, 6, 4, 5, 3, 5, 3, 8, 5, 4, 4, 2, 3, 0, 1, 3, 6, 1, 1, 8, 8, 9, 5, 7, 3, 0, 8, 5, 4, 9, 2, 7, 9, 8, 9, 3, 4, 7, 5

Offset

-6,1

Comments

The probability P{(x-m)/s > 5} for a normally distributed random variable x with mean m and standard deviation s.

In experimental sciences (hypothesis testing), a measured excursion exceeding background "noise" by more than five standard deviations is considered practically certain, unless it is an isolated case among tens of thousands of iterated measurements.

Links

Stanislav Sykora, Table of n, a(n) for n = -6..1994

Wikipedia, Normal distribution

Formula

P{(x-m)/s > 5} = P{(x-m)/s < -5} = 0.5*erfc(5/sqrt(2)), with erfc(x) being the complementary error function.

Example

2.86651571879193911673752332874645353854423013611889573...e-7

Mathematica

First[RealDigits[1 - CDF[NormalDistribution[], 5], 10, 100]] (* Joan Ludevid, Jun 13 2022 *)

Prog

(PARI) n=5; a=0.5*erfc(n/sqrt(2))  \\ Use sufficient realprecision

Crossrefs

Cf. P{(x-m)/s>n}: A239382 (n=1), A239383 (n=2), A239384 (n=3), A239385 (n=4), A239387 (n=6).

Sequence in context: A021353 A131361 A228042 * A011370 A021890 A199504

Adjacent sequences: A239383 A239384 A239385 * A239387 A239388 A239389

Keyword

nonn,cons

Author

Stanislav Sykora, Mar 18 2014

Status

approved